Modified Exponential Power distribution with properties and applications

Abstract

We have developed the Modified Exponential power distribution, a new and adaptable probability distribution, in this work. An additional shape parameter is added to the exponential power distribution to create this distribution. Numerous statistical properties of suggested model are derived and analyzed. Cramer-Von-Mises (CVME), maximum likelihood (MLE), and least-squares (LSE) are used to estimate the model's parameters. P-P and Q-Q charts are used to assess the validity of the model. Several information criteria are applied in model comparisons, including the Bayesian Information Criterion (BIC), the Hannan-Quinn Information Criterion (HQIC), the Corrected Akaike Information Criterion (CAIC), and the Akaike Information Criterion (AIC). These criteria help determine the best model by balancing goodness-of-fit with model complexity. Test statistics, together with their corresponding p-values, are also utilized to evaluate the recommended model's goodness of fit. These tests consist of the Kolmogorov-Smirnov (KS), Cramer-Von Mises (CVM), and Anderson-Darling (An) tests. R programming is used for the dataset analysis and visualization.